Dynamics Analysis of a Stochastic Delay Gilpin-Ayala Model with Markovian Switching
This paper considers a stochastic delay Gilpin-Ayala model with Markovian switching. Using Lyapunov method, we show existence and uniqueness of global positive solution. Then, by using Chebyshev’s inequality, M-matrix method, and BDG’s inequality, stochastic permanence and asymptotic estimations of...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2019/1302648 |
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| _version_ | 1832561679791030272 |
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| author | Qiaoqin Gao Zhijiang Luo Guirong Liu |
| author_facet | Qiaoqin Gao Zhijiang Luo Guirong Liu |
| author_sort | Qiaoqin Gao |
| collection | DOAJ |
| description | This paper considers a stochastic delay Gilpin-Ayala model with Markovian switching. Using Lyapunov method, we show existence and uniqueness of global positive solution. Then, by using Chebyshev’s inequality, M-matrix method, and BDG’s inequality, stochastic permanence and asymptotic estimations of solutions are studied. Finally, numerical simulations illustrate the theoretical results. Our results generalize and improve the existing results. |
| format | Article |
| id | doaj-art-02adfc06628b4c0a9cc0b173762cf08d |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-02adfc06628b4c0a9cc0b173762cf08d2025-02-03T01:24:23ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2019-01-01201910.1155/2019/13026481302648Dynamics Analysis of a Stochastic Delay Gilpin-Ayala Model with Markovian SwitchingQiaoqin Gao0Zhijiang Luo1Guirong Liu2Department of Mathematics, Luliang University, Lishi, Shanxi 033001, ChinaDepartment of Mathematics, Luliang University, Lishi, Shanxi 033001, ChinaSchool of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, ChinaThis paper considers a stochastic delay Gilpin-Ayala model with Markovian switching. Using Lyapunov method, we show existence and uniqueness of global positive solution. Then, by using Chebyshev’s inequality, M-matrix method, and BDG’s inequality, stochastic permanence and asymptotic estimations of solutions are studied. Finally, numerical simulations illustrate the theoretical results. Our results generalize and improve the existing results.http://dx.doi.org/10.1155/2019/1302648 |
| spellingShingle | Qiaoqin Gao Zhijiang Luo Guirong Liu Dynamics Analysis of a Stochastic Delay Gilpin-Ayala Model with Markovian Switching Discrete Dynamics in Nature and Society |
| title | Dynamics Analysis of a Stochastic Delay Gilpin-Ayala Model with Markovian Switching |
| title_full | Dynamics Analysis of a Stochastic Delay Gilpin-Ayala Model with Markovian Switching |
| title_fullStr | Dynamics Analysis of a Stochastic Delay Gilpin-Ayala Model with Markovian Switching |
| title_full_unstemmed | Dynamics Analysis of a Stochastic Delay Gilpin-Ayala Model with Markovian Switching |
| title_short | Dynamics Analysis of a Stochastic Delay Gilpin-Ayala Model with Markovian Switching |
| title_sort | dynamics analysis of a stochastic delay gilpin ayala model with markovian switching |
| url | http://dx.doi.org/10.1155/2019/1302648 |
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